OK, so I though this was a VirtIO misdetection, but even when I manually select VirtIO, Cloudmin gets the interface name wrong (still names it eth0).
Since this is a Debian image, Cloudmin is editing the /etc/network/interfaces file, which before editing by Cloudmin contains the following:
# This file describes the network interfaces available on your system
# and how to activate them. For more information, see interfaces(5).
# The loopback network interface
iface lo inet loopback
# The primary network interface
iface ens3 inet dhcp
So...seems like Cloudmin ought to figure out that iface = ens3
If it picked up that info, it'd be able to create a function network config out of the box.